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<div class="title">group_lattice.h</div>  </div>
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<div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160;<span class="preprocessor">#ifndef GROUP_LATTICE</span></div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="preprocessor"></span><span class="preprocessor">#define GROUP_LATTICE</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="preprocessor"></span></div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="preprocessor">#include &lt;vector&gt;</span></div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="preprocessor">#include &lt;map&gt;</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="preprocessor">#include &lt;boost/math/special_functions/prime.hpp&gt;</span></div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="preprocessor">#include &lt;cassert&gt;</span></div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="preprocessor">#include &quot;std_ex.h&quot;</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="preprocessor">#include &quot;subgroup.h&quot;</span></div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;</div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="keyword">template</span> &lt;<span class="keyword">typename</span> G&gt;</div>
<div class="line"><a name="l00016"></a><span class="lineno"><a class="line" href="classcGrpLattice.html">   16</a></span>&#160;<span class="keyword">class </span><a class="code" href="classcGrpLattice.html">cGrpLattice</a></div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160;{</div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160;<span class="keyword">public</span>:</div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;</div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> G::ElementType T;</div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> std::vector&lt; cSubgroup&lt;G&gt; &gt;::iterator SubGrp_Iterator;</div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;    <span class="keyword">typedef</span> <a class="code" href="classcGrpLattice.html">cGrpLattice&lt;G&gt;</a> <a class="code" href="classcGrpLattice.html">SelfType</a>;</div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;    <span class="keyword">typedef</span> <span class="keyword">typename</span> std::vector&lt;T&gt; ElemVec;</div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160;</div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;    <a class="code" href="classcGrpLattice.html">cGrpLattice</a>(G &amp;group)</div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;        :m_Group(group)</div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160;    {};</div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;    ~<a class="code" href="classcGrpLattice.html">cGrpLattice</a>()</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160;    {};</div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160;    <span class="keyword">friend</span> std::ostream&amp; operator&lt;&lt;(std::ostream&amp; out, <a class="code" href="classcGrpLattice.html">SelfType</a>&amp; lattice)</div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;    {</div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;        out&lt;&lt;<span class="stringliteral">&quot;LATTICE:\n&quot;</span>;</div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;        <span class="keywordflow">for</span>(<span class="keywordtype">int</span> index = lattice.m_Lattice.size() - 1; index &gt;= 0; index--)</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160;        {</div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;            std::vector&lt; cSubgroup&lt;G&gt; &gt; layer = lattice.GetLayer(index);</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;            out&lt;&lt;<span class="stringliteral">&quot;Layer &quot;</span>&lt;&lt;index&lt;&lt;<span class="stringliteral">&quot; : \n&quot;</span>;</div>
<div class="line"><a name="l00039"></a><span class="lineno">   39</span>&#160;            <span class="keywordflow">for</span>(SubGrp_Iterator iter = layer.begin(); iter != layer.end(); iter++)</div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;            {</div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;                out&lt;&lt;*iter&lt;&lt;<span class="stringliteral">&quot;\n&quot;</span>;</div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;            }</div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160;        }</div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;        <span class="keywordflow">return</span> out;</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;    };</div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160;</div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;</div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;    std::vector&lt; cSubgroup&lt;G&gt; &gt;&amp; GetLayer(<span class="keyword">const</span> std::size_t index)</div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;    {</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;        assert(m_Lattice.size() &gt; index);</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;        <span class="keywordflow">return</span> m_Lattice[index];</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;    };</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160;</div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;</div>
<div class="line"><a name="l00055"></a><span class="lineno">   55</span>&#160;    <span class="keywordtype">void</span> CyclicExtensionMethod()</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160;    {</div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;        BuildCycSubgrpPPOrder();</div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;</div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;        AddFirstLayer();</div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160;</div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;        <span class="comment">//cyclic subgroups of prime power order</span></div>
<div class="line"><a name="l00062"></a><span class="lineno">   62</span>&#160;        AddSecondLayer();</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160;</div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;        <span class="keywordtype">bool</span> need_new_layer = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;        <span class="comment">//main loop -- iterate through every layer</span></div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160;        <span class="keywordflow">for</span>(std::size_t index = 1; index &lt; m_Non_Triv_Layers; index++)</div>
<div class="line"><a name="l00067"></a><span class="lineno">   67</span>&#160;        {</div>
<div class="line"><a name="l00068"></a><span class="lineno">   68</span>&#160;            <span class="comment">//add cyclic subgroups of order p^index</span></div>
<div class="line"><a name="l00069"></a><span class="lineno">   69</span>&#160;            <span class="keywordflow">if</span>(m_CycSubgrpsGen[index+1].empty())</div>
<div class="line"><a name="l00070"></a><span class="lineno">   70</span>&#160;            {</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;                need_new_layer = <span class="keyword">true</span>;</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160;            }</div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;            <span class="keywordflow">else</span></div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;            {</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160;                AddNewLayer();</div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;                <span class="keywordflow">for</span>(<span class="keyword">typename</span> ElemVec::iterator it = m_CycSubgrpsGen[index+1].begin();</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;                        it != m_CycSubgrpsGen[index+1].end(); it++)</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;                {</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;                    <a class="code" href="classcSubgroup.html">cSubgroup&lt;G&gt;</a> subgrp;</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;                    subgrp.AddGenerator(*it);</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;                    GetLayer(index+1).push_back(subgrp);</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;                }</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160;            }</div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;            <span class="comment">//for each subgroup in the layer</span></div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;            <span class="keywordflow">for</span>(SubGrp_Iterator subgrp_iter = GetLayer(index).begin();</div>
<div class="line"><a name="l00086"></a><span class="lineno">   86</span>&#160;                    subgrp_iter != GetLayer(index).end(); subgrp_iter++)</div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;            {</div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;                <span class="comment">//compute generators of possible subgroups</span></div>
<div class="line"><a name="l00089"></a><span class="lineno">   89</span>&#160;                <span class="comment">//possible_gen = (cyc_gen ^ (N(U) - U) ) - subgrps in the ith layer</span></div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;                ElemVec norm_elem = m_Group.GetNormalizerEl(*subgrp_iter);</div>
<div class="line"><a name="l00091"></a><span class="lineno">   91</span>&#160;                <span class="comment">//std_ex::print_vector(norm_elem);</span></div>
<div class="line"><a name="l00092"></a><span class="lineno">   92</span>&#160;</div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;                std_ex::set_difference(norm_elem, (*subgrp_iter).GetElementsDimino());</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;</div>
<div class="line"><a name="l00095"></a><span class="lineno">   95</span>&#160;</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;                <span class="comment">//std_ex::print_vector(norm_elem);</span></div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;                ElemVec possible_gen = std_ex::set_intersection(m_CycSubgrpsGen[1],</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160;                                       norm_elem);</div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;                <span class="comment">//remove subgroups already in the ith layer</span></div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;                <span class="keywordflow">if</span>(index+1 &lt; m_Lattice.size())</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;                {</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;                    <span class="keywordflow">for</span>(SubGrp_Iterator subgrp1_iter = GetLayer(index+1).begin();</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;                            subgrp1_iter != GetLayer(index+1).end(); subgrp1_iter++)</div>
<div class="line"><a name="l00106"></a><span class="lineno">  106</span>&#160;                    {</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160;                        std_ex::set_difference(possible_gen,</div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;                                               (*subgrp1_iter).GetGeneratorsSet());</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;                    }</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160;                }</div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160;</div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160;                <span class="comment">//construct new subgroups and add them to the ith layer</span></div>
<div class="line"><a name="l00113"></a><span class="lineno">  113</span>&#160;                <span class="keywordflow">while</span>(!possible_gen.empty())</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160;                {</div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;                    T generator = *possible_gen.begin();</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;                    <span class="keywordflow">if</span>(Has_prime_pow_el(*subgrp_iter, generator))</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160;                    {</div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;                        <a class="code" href="classcSubgroup.html">cSubgroup&lt;G&gt;</a> subgrp = (*subgrp_iter);</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160;                        subgrp.AddGenerator(generator);</div>
<div class="line"><a name="l00120"></a><span class="lineno">  120</span>&#160;                        <span class="keywordflow">if</span>(need_new_layer)</div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;                        {</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160;                            AddNewLayer();</div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;                            need_new_layer = <span class="keyword">false</span>;</div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;                        }</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;                        GetLayer(index+1).push_back(subgrp);</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160;                        std_ex::set_difference(possible_gen,subgrp.GetElementsDimino());</div>
<div class="line"><a name="l00127"></a><span class="lineno">  127</span>&#160;                    }</div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;                    <span class="keywordflow">else</span></div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160;                    {</div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160;                        possible_gen.erase(possible_gen.begin());</div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160;                    }</div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160;                }</div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160;            }</div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;        }</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160;        AddLastLayer();</div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;    };</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160;</div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;<span class="keyword">private</span>:</div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160;</div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;    <span class="comment">//add a new empty layer</span></div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;    <span class="keywordtype">void</span> AddNewLayer()</div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;    {</div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;        std::vector&lt; cSubgroup&lt;G&gt; &gt; new_layer;</div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;        m_Lattice.push_back(new_layer);</div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;    };</div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;</div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;    <span class="comment">//add first layer containing the subgroup</span></div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;    <span class="comment">//generated by the identity</span></div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;    <span class="keywordtype">void</span> AddFirstLayer()</div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;    {</div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;        ElemVec trivial_subgrp_gen;</div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;        trivial_subgrp_gen.push_back(m_Group.GetIdentity());</div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;        <a class="code" href="classcSubgroup.html">cSubgroup&lt;G&gt;</a> trivial_subgrp(trivial_subgrp_gen);</div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;        std::vector&lt; cSubgroup&lt;G&gt; &gt; layer0;</div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;        layer0.push_back(trivial_subgrp);</div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;        m_Lattice.push_back(layer0);</div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;    };</div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;</div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;    <span class="comment">//add second layer consisting of cyclic? subgroups</span></div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;    <span class="comment">//of prime power order</span></div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;    <span class="keywordtype">void</span> AddSecondLayer()</div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;    {</div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;        AddNewLayer();</div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;</div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;        <span class="keywordflow">for</span>(<span class="keyword">typename</span> ElemVec::iterator iter = m_CycSubgrpsGen[1].begin();</div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;                iter != m_CycSubgrpsGen[1].end(); iter++)</div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;        {</div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;            <a class="code" href="classcSubgroup.html">cSubgroup&lt;G&gt;</a> newsubgroup;</div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;            newsubgroup.AddGenerator(*iter);</div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;            assert(isPrime(newsubgroup.GetCyclicSubgroup(*iter).size()));</div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;            m_Lattice[1].push_back(newsubgroup);</div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;        }</div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;    };</div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;</div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;    <span class="comment">//add last layer containing the group G itself</span></div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;    <span class="keywordtype">void</span> AddLastLayer()</div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;    {</div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;        AddNewLayer();</div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;        <a class="code" href="classcSubgroup.html">cSubgroup&lt;G&gt;</a> group_itself(m_Group);</div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;        m_Lattice[m_Lattice.size()-1].push_back(group_itself);</div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;    };</div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;</div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;    <span class="comment">//build cyclic subgroups of prime power order</span></div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;    <span class="comment">//also computes the number of non-trivial layers</span></div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;    <span class="keywordtype">void</span> BuildCycSubgrpPPOrder()</div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;    {</div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;        ElemVec group_elements = m_Group.GetElementsDimino();</div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;</div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;        <span class="comment">//set the number of non-trivial layers</span></div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;        <span class="comment">//factor the group order -- TODO : improve algorithm</span></div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;        <span class="comment">//trial division -- bad complexity</span></div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;        std::size_t group_order = group_elements.size();</div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;        std::size_t index1 = 0;</div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;        std::size_t non_triv_layers = 0;</div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;        <span class="keywordflow">while</span>(group_order &gt; 1)</div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;        {</div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;            std::size_t prime = boost::math::prime(index1);</div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;            <span class="keywordflow">while</span>(group_order % prime == 0)</div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;            {</div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;                group_order = group_order / prime;</div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160;                non_triv_layers++;</div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;            }</div>
<div class="line"><a name="l00203"></a><span class="lineno">  203</span>&#160;            index1++;</div>
<div class="line"><a name="l00204"></a><span class="lineno">  204</span>&#160;        }</div>
<div class="line"><a name="l00205"></a><span class="lineno">  205</span>&#160;        m_Non_Triv_Layers = non_triv_layers - 1;</div>
<div class="line"><a name="l00206"></a><span class="lineno">  206</span>&#160;</div>
<div class="line"><a name="l00207"></a><span class="lineno">  207</span>&#160;</div>
<div class="line"><a name="l00208"></a><span class="lineno">  208</span>&#160;        <span class="keywordflow">while</span>(!group_elements.empty())</div>
<div class="line"><a name="l00209"></a><span class="lineno">  209</span>&#160;        {</div>
<div class="line"><a name="l00210"></a><span class="lineno">  210</span>&#160;            ElemVec cyc_subgrp_elem = m_Group.GetCyclicSubgroup(*group_elements.begin());</div>
<div class="line"><a name="l00211"></a><span class="lineno">  211</span>&#160;            std::size_t cyc_subgrp_size = cyc_subgrp_elem.size();</div>
<div class="line"><a name="l00212"></a><span class="lineno">  212</span>&#160;            <span class="keywordflow">if</span>(isPrime(cyc_subgrp_size))</div>
<div class="line"><a name="l00213"></a><span class="lineno">  213</span>&#160;            {</div>
<div class="line"><a name="l00214"></a><span class="lineno">  214</span>&#160;                m_CycSubgrpsGen[1].push_back(*group_elements.begin());</div>
<div class="line"><a name="l00215"></a><span class="lineno">  215</span>&#160;            }</div>
<div class="line"><a name="l00216"></a><span class="lineno">  216</span>&#160;            <span class="keywordflow">else</span></div>
<div class="line"><a name="l00217"></a><span class="lineno">  217</span>&#160;            {</div>
<div class="line"><a name="l00218"></a><span class="lineno">  218</span>&#160;                std::size_t index = 0;</div>
<div class="line"><a name="l00219"></a><span class="lineno">  219</span>&#160;                std::size_t power = 0;</div>
<div class="line"><a name="l00220"></a><span class="lineno">  220</span>&#160;                <span class="keywordflow">while</span>(cyc_subgrp_size &gt; 1)</div>
<div class="line"><a name="l00221"></a><span class="lineno">  221</span>&#160;                {</div>
<div class="line"><a name="l00222"></a><span class="lineno">  222</span>&#160;                    std::size_t prime = boost::math::prime(index);</div>
<div class="line"><a name="l00223"></a><span class="lineno">  223</span>&#160;                    <span class="keywordflow">while</span>(cyc_subgrp_size % prime == 0)</div>
<div class="line"><a name="l00224"></a><span class="lineno">  224</span>&#160;                    {</div>
<div class="line"><a name="l00225"></a><span class="lineno">  225</span>&#160;                        cyc_subgrp_size = cyc_subgrp_size / prime;</div>
<div class="line"><a name="l00226"></a><span class="lineno">  226</span>&#160;                        power++;</div>
<div class="line"><a name="l00227"></a><span class="lineno">  227</span>&#160;                    }</div>
<div class="line"><a name="l00228"></a><span class="lineno">  228</span>&#160;                    index++;</div>
<div class="line"><a name="l00229"></a><span class="lineno">  229</span>&#160;                }</div>
<div class="line"><a name="l00230"></a><span class="lineno">  230</span>&#160;                m_CycSubgrpsGen[power].push_back(*group_elements.begin());</div>
<div class="line"><a name="l00231"></a><span class="lineno">  231</span>&#160;            }</div>
<div class="line"><a name="l00232"></a><span class="lineno">  232</span>&#160;            <span class="comment">//TODO</span></div>
<div class="line"><a name="l00233"></a><span class="lineno">  233</span>&#160;            std_ex::set_difference(group_elements, cyc_subgrp_elem);</div>
<div class="line"><a name="l00234"></a><span class="lineno">  234</span>&#160;        }</div>
<div class="line"><a name="l00235"></a><span class="lineno">  235</span>&#160;</div>
<div class="line"><a name="l00236"></a><span class="lineno">  236</span>&#160;    };</div>
<div class="line"><a name="l00237"></a><span class="lineno">  237</span>&#160;</div>
<div class="line"><a name="l00238"></a><span class="lineno">  238</span>&#160;    <span class="comment">//check if a subgroup contains the element at prime power order</span></div>
<div class="line"><a name="l00239"></a><span class="lineno">  239</span>&#160;    <span class="keywordtype">bool</span> Has_prime_pow_el(<span class="keyword">const</span> <a class="code" href="classcSubgroup.html">cSubgroup&lt;G&gt;</a> grp, <span class="keyword">const</span> T element)<span class="keyword">const</span></div>
<div class="line"><a name="l00240"></a><span class="lineno">  240</span>&#160;<span class="keyword">    </span>{</div>
<div class="line"><a name="l00241"></a><span class="lineno">  241</span>&#160;        std::size_t prime_index = 0;</div>
<div class="line"><a name="l00242"></a><span class="lineno">  242</span>&#160;        std::size_t elem_order = element.GetOrder();</div>
<div class="line"><a name="l00243"></a><span class="lineno">  243</span>&#160;        std::size_t prime = boost::math::prime(prime_index);</div>
<div class="line"><a name="l00244"></a><span class="lineno">  244</span>&#160;        <span class="keywordflow">while</span>(prime &lt;= elem_order)</div>
<div class="line"><a name="l00245"></a><span class="lineno">  245</span>&#160;        {</div>
<div class="line"><a name="l00246"></a><span class="lineno">  246</span>&#160;            <span class="keywordflow">if</span>(grp.Contains(element.GetNthPower(prime)))</div>
<div class="line"><a name="l00247"></a><span class="lineno">  247</span>&#160;                <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00248"></a><span class="lineno">  248</span>&#160;            prime_index++;</div>
<div class="line"><a name="l00249"></a><span class="lineno">  249</span>&#160;            prime = boost::math::prime(prime_index);</div>
<div class="line"><a name="l00250"></a><span class="lineno">  250</span>&#160;        }</div>
<div class="line"><a name="l00251"></a><span class="lineno">  251</span>&#160;        <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00252"></a><span class="lineno">  252</span>&#160;    };</div>
<div class="line"><a name="l00253"></a><span class="lineno">  253</span>&#160;</div>
<div class="line"><a name="l00254"></a><span class="lineno">  254</span>&#160;    <span class="comment">//TODO -- improve naive primality testing</span></div>
<div class="line"><a name="l00255"></a><span class="lineno">  255</span>&#160;    <span class="keywordtype">bool</span> isPrime(<span class="keywordtype">int</span> number)</div>
<div class="line"><a name="l00256"></a><span class="lineno">  256</span>&#160;    {</div>
<div class="line"><a name="l00257"></a><span class="lineno">  257</span>&#160;        <span class="keywordflow">if</span>(number == 2) <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00258"></a><span class="lineno">  258</span>&#160;        <span class="keywordflow">if</span>(number == 1 || (number%2 == 0)) <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00259"></a><span class="lineno">  259</span>&#160;        <span class="keywordflow">for</span>(<span class="keywordtype">int</span> i=3; i*i&lt;=number; i+=2)</div>
<div class="line"><a name="l00260"></a><span class="lineno">  260</span>&#160;        {</div>
<div class="line"><a name="l00261"></a><span class="lineno">  261</span>&#160;            <span class="keywordflow">if</span>(number%i == 0)</div>
<div class="line"><a name="l00262"></a><span class="lineno">  262</span>&#160;                <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00263"></a><span class="lineno">  263</span>&#160;        }</div>
<div class="line"><a name="l00264"></a><span class="lineno">  264</span>&#160;        <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00265"></a><span class="lineno">  265</span>&#160;    }</div>
<div class="line"><a name="l00266"></a><span class="lineno">  266</span>&#160;</div>
<div class="line"><a name="l00267"></a><span class="lineno">  267</span>&#160;<span class="keyword">private</span>:</div>
<div class="line"><a name="l00268"></a><span class="lineno">  268</span>&#160;    G                                               m_Group;</div>
<div class="line"><a name="l00269"></a><span class="lineno">  269</span>&#160;    std::map&lt;int, ElemVec&gt;                          m_CycSubgrpsGen;</div>
<div class="line"><a name="l00270"></a><span class="lineno">  270</span>&#160;    std::vector&lt; std::vector&lt; cSubgroup&lt;G&gt; &gt; &gt;      m_Lattice;</div>
<div class="line"><a name="l00271"></a><span class="lineno">  271</span>&#160;    std::size_t                                     m_Non_Triv_Layers;</div>
<div class="line"><a name="l00272"></a><span class="lineno">  272</span>&#160;};</div>
<div class="line"><a name="l00273"></a><span class="lineno">  273</span>&#160;</div>
<div class="line"><a name="l00274"></a><span class="lineno">  274</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00275"></a><span class="lineno">  275</span>&#160;<span class="preprocessor"></span></div>
<div class="ttc" id="classcSubgroup_html"><div class="ttname"><a href="classcSubgroup.html">cSubgroup</a></div><div class="ttdef"><b>Definition:</b> subgroup.h:5</div></div>
<div class="ttc" id="classcGrpLattice_html"><div class="ttname"><a href="classcGrpLattice.html">cGrpLattice</a></div><div class="ttdef"><b>Definition:</b> group_lattice.h:16</div></div>
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